Draft a lesson plan that still works when half the class already gets it and half doesn't

You are helping me draft a lesson plan for one class period, and I need it to actually work for a mixed-readiness classroom — not assume every student is at the same starting point.

SUBJECT AND GRADE LEVEL
7th grade math

LEARNING OBJECTIVE FOR THIS PERIOD
Students can solve two-step linear equations involving negative coefficients

CLASS PERIOD LENGTH
50 minutes

WHAT I KNOW ABOUT THE READINESS SPREAD
About a third can already do one-step equations fluently; a third are shaky on integer operations, which will make negative coefficients hard regardless of the new content

MATERIALS I ALREADY HAVE ACCESS TO
Whiteboards for pairs, a class set of Chromebooks, no printer access today

Build the lesson in four timed segments: a hook (short, tied directly to Students can solve two-step linear equations involving negative coefficients, not a generic warm-up unrelated to today's content), direct instruction, guided practice, and independent practice — give each segment a specific minute allocation that sums to 50 minutes. For the independent practice segment specifically, write two parallel tracks based on About a third can already do one-step equations fluently; a third are shaky on integer operations, which will make negative coefficients hard regardless of the new content: a "core task" every student attempts, and an explicit branch — an extension task for students who finish the core task early that goes deeper on the same objective rather than just being "more of the same, but harder," and a scaffolded version of the core task for students who are struggling, that removes one specific source of difficulty rather than just simplifying everything. Name the exact trigger for switching a student onto either branch (e.g., "finishes the core task with 8+ minutes left" or "stuck on step 2 for more than 3 minutes") — a branch nobody can identify when to use in the moment doesn't actually get used. Write one formative check — something you can observe or collect in under 2 minutes — that tells you by the end of the period whether Students can solve two-step linear equations involving negative coefficients actually landed, distinct from just asking "any questions?"

WHAT NOT TO DO
Do not write generic classroom-management language ("engage students," "foster a positive environment") — every line should be a concrete instructional move. Do not assume materials beyond Whiteboards for pairs, a class set of Chromebooks, no printer access today are available.

OUTPUT FORMAT
1. Table: segment, minutes, what the teacher does, what students do.
2. The independent-practice branch: core task, early-finisher extension with its trigger, and struggling-student scaffold with its trigger.
3. The formative check and what result would mean the objective didn't land.